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Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.2. Second-Order Quasilinear Hyperbolic Equations
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}-
\left(\frac 1w\frac{\partial w}{\partial t}+b\right)\frac{\partial w}{\partial x}-\frac{c}{w}\frac{\partial w}{\partial t}-c b= 0$.
%where $b$ and $c$ are constants.
The general solution:\hfill\break
$\displaystyle w(t,x) = \left\{-c\int\,\exp[-e^{bt}G(x)]\,dx+F(t)\right\}\exp[e^{bt}G(x)]$,\hfill\break
where $F(t)$ and $G(x)$ are arbitrary functions.
Remarks:This PDE is particular case of PDEs family EQ 19
Novelty:Material has been fully published elsewhere
References:Yu.N. Kosovtsov. The general solutions of some nonlinear second and third order PDEs with constant and nonconstant parameters. (2006).
Author/Contributor's Details
Last name:Kosovtsov
First name:Yurii
Statistic information
Submission date:Mon 11 Dec 2006 08:54
Edits by author:1
Last edit by author:Mon 11 Dec 2006 12:10

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